An investigator analyzed the leading digits from 784 checks issued by seven suspect companies. The frequencies were found to be 2, 15, 0, 73, 496, 163, 9, 22, and 5, and those digits correspond to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively. If the observed frequencies are substantially different from the frequencies expected with Benford's law shown below, the check amounts appear to result from fraud. Use a 0.025 significance level to test for goodness-of-fit with Benford's law. Does it appear that the checks are the result of fraud? Leading Digit Actual Frequency Benford's Law: Distribution of Leading Digits 2 15 17.6% 73 9.7% 5 495 7.9% 6. 163 6.7% 6. 5.8% 22 5.1% 30.1% 12.5% 4.6% Determine the null and alternative hypotheses Ho At least two leading digits have frequencies that do not conform to Benford's law. The leading digits are from a population that conforms to Benford's law. At most three leading digits have frequencies that do not conform to Benford's law. At least one leading digit has a frequency that does not conform to Benford's law.

Please give a detailed explanation, not just the answer. Thanks in advance! You are conducting a study to see if the proportion of men over the age of 50 who regularly have their prostate examined is significantly less than 0.31. A random sample of 709 men over the age of 50 found that 207 have their prostate regularly examined. Do the sample data provide convincing evidence to support the claim? Test the relevant hypotheses using a 1% level of significance. Give answer to at least 4 decimal places. a. What are the correct hypotheses? (Select the correct symbols and use decimal values not percentages.)H0: Select an answer μ σ σ² s² x̄ p p̂ s   ? < ≠ ≤ > ≥ =   H1: Select an answer σ μ s² σ² p̂ x̄ p s   ? > ≤ ≠ < = ≥    b. Based on the hypotheses, find the following: Test Statistic = Critical-value= c. Shade the sampling distribution curve with the correct critical value(s) and shade the critical regions.    d. The correct summary would be: Select an answer There is not…

Please show all work so I can understand!

could you please tell me how to explain to a friend who does not know anything about statistics the relationship between the confidence level expressed as a confidence interval and the level of significance in hypothesis testing. Illustrate the relationship using either the critical value or the p-value approach.thanks

The data below comes from a university that wanted to see if there was a relationship between High School GPA and College GPA. For each hypothesis test, provide the claim, critical values, test statistic and conclusion.1) Using a 95% level of confidence, test the claim High School GPA’s have a mean of 3.0.2) Using a 95% level of confidence, test the claim College GPA’s have a mean of 3.0.3) Using a 95% level of confidence, test the claim that the majority of students have at least a 3.0 GPA in High School. High School           College GPAGPA3.88                            3.713.20                            2.982.88                            2.713.95                            3.744.1                              4.03.9                               3.813.4                               3.332.77                             2.643.55                            3.363.45                            3.353.05                            2.973.94                            3.83.65…

Hi Expert, I need your help on my term project.  I do not know which method and which statistical test to use to analyze the data I have collected for my term project.  I have collected data for my hypothesis: Are Christian men attending church less than Christian women? First church: 33 men, 38 women Second church: 49 men, 63 women Below is the requirement from my instructor: Inference (Conclusion from findings):Check appropriate conditions for your test of significance (if application)Show all applicable work: Sampling Distribution, Test Statistic Calculation,p-value, etc.Answer your research question based on your inferential calculations.· Interpret the exploratory data analysis in the context of your research question.    Thank you very much for your help, :)

I need the test static, critical value , null & alternative hypothesis , conclusion & also probably p value Thankyou so much I need help kn working these out.

Please help with 1-8! I've seen a bunch of different answers and would love work shown so I can understand. Thank you! 1. are the samples dependent or independent? 2. State null/alternative hypotheses 3. what is the test statistic? 4. What is the p-value? 5. What are the critical values? 6. Does the test statistic lie in the rejection region? 7. interpret the results 8: does the result change for a different value of alpha? Explain

What do confidence intervals & hypothesis tests try to do?

Calculate the test statistic for the test of hypotheses